Respuesta :
Answer:
Admission fee charged = $3
Cost of each ride = $10
Step-by-step explanation:
Let admission fee charged by amusement park in dollars be =[tex]x[/tex]
Let cost of each ride in dollars be =[tex]y[/tex]
Given:
Admission plus four rides cost $22
If each ride cost in dollars = [tex]y[/tex]
Cost of 4 rides in dollars will be = [tex]4y[/tex]
So, the total cost in dollars will be given as =[tex]x+4y[/tex]
So, we have
[tex]x+4y=22[/tex]
Admission plus seven ride cost $31.
If each ride cost in dollars = [tex]y[/tex]
Cost of 7 rides in dollars will be = [tex]7y[/tex]
So, the total cost in dollars will be given as =[tex]x+7y[/tex]
So, we have
[tex]x+7y=31[/tex]
So, we have the system of equation as:
A) [tex]x+4y=22[/tex]
B) [tex]x+7y=31[/tex]
Solving the system by elimination method.
Eliminating [tex]x[/tex] by subtracting equation A from B.
[tex]x+7y=31[/tex]
- [tex]x+4y=22[/tex]
- - - [Sign of each term of subtract-ant gets reversed]
-----------------------------
[tex]3y=9[/tex]
Dividing both sides by 3.
[tex]\frac{3y}{3}=\frac{9}{3}[/tex]
∴ [tex]y=3[/tex]
Plugging in [tex]y=3[/tex] in equation A.
[tex]x+4(3)=22[/tex]
[tex]x+12=22[/tex]
Subtracting both sides by 12.
[tex]x+12-12=22-12[/tex]
∴ [tex]x=10[/tex]
Thus, admission fee charged = $3
Cost of each ride = $10
